I'm reading a paper on semi-simple Lie group geometry at the moment, but finding the going a bit tough since I'm missing alot of the prerequisites. Firstly, the author refers to a *principal embedding* of one Lie group into another. I guess that this is an embedding of one group into another that is maximal in some sense (he hints at a relation to Dynkin diagrams). I've searched the web but can't find a principal embedding defn, could someone point me in the right direction.

Secondly, if $G_0$ is principal embedded into $G$, is there some result about the quotient $G/G_0$ having a complex structure?